A "product digit-day" is a date in which the respective product of the digits of the month and the day multiply up to the product of the digits of the year in the mm-dd-yy format.

For example,12-18-28 is a product digit-day as the respective product of the digits of the month and the day multiply up to 16 which is equal to the product of the digits of the year.

(i) Determine the total number of product digit-days from January 1, 2001 to December 31, 2099 inclusively.

(ii) Determine the year(s) having the maximum number of product digit-days in the period covered under (i).

(iii) Determine the last product digit-day in the period covered under (i).